A thermoplastic elastomer has not been required to have scratch resistance, because a molded article obtained by molding the thermoplastic elastomer is used after coating thereon with a coating agent, and the coated layer has scratch resistance. In recent years, there are less and less articles having such a coated layer, therefore, scratch resistance of material is highly regarded, and, in some cases, their abrasion resistance is also highly regarded in addition to the scratch resistance. And, their levels required are becoming higher and higher. Taking the present condition into consideration, it is difficult to say that a conventional process for producing a thermoplastic elastomer is always satisfactory.